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Stability of Infinite Dimensional Stochastic Differential Equations with Applications

Stability of Infinite Dimensional Stochastic Differential  Equations with Applications by Kai Liu
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Preface

STOCHASTIC DIFFERENTIAL EQUATIONS IN INFINITE DIMENSIONS
Notations,Definitions and Preliminaries
Wiener Processes and Stochastic Integration
Definitions and Methods of Stability
Notes and Comments

STABILITY F LINEAR STOCHASTIC DIFFERENTIAL EQUATIONS
Stable Semigroups
Lyapunov Equations and Stability
Uniformly Asymptotic Stability

STABILITY F NONLINEAR STOCHASTIC DIFFERENTIAL EQUATIONS
Equivalence of L p -Stability and Exponential Stability
A Coerciv Decay Condition
Stability of Semilinear Stochastic Evolution Equations
Lyapunov Functions for Strong Solutions
Two Applications
Further Results on Invariant Measures
Stability,Ultimate Boundedness of Mild Solutions and Invariant Measures
Decay Rates of Systems
Stabilization of Systems by Noise
Lyapunov Exponents and Stabilization
Notes and Comments

STABILITY OF STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS
Linear Deterministic Equations
Stability Equivalence and Reduction of Neutral Equations .
Decay Criteria of Stochastic Delay Differential Equations
Razumikhin Type Stability Theorems
Notes and Comments

SOME RELATED TOPICS OF STABILITY AND APPLICATIONS
Parabolic Equations with Boundary and Pointwise Noise
Stochastic Stability and Quadratic Control
Feedback Stabilization of Stochastic Differential Equations
Stochastic Models in Mathematical Physics
Stochastic Systems Related to Multi-Species Population Dynamics
Notes and Comments

Appendix A: The Proof of Proposition
Appendix B: Existence and Uniqueness of Strong Solutions of Stochastic Delay Differential Equations
References
Index
CRC Press; August 2005
311 pages; ISBN 9781420034820
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Title: Stability of Infinite Dimensional Stochastic Differential Equations with Applications
Author: Kai Liu
 
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